MATH107 Math in Society Spring 2009
Turn in FINAL DRAFTS of these problems. Your finished product should be easy to read and contain how you reached your answers (show work).
Functions
1. Complete the Excursion on p. 360.
2. An egg rancher has determined that the weekly sales of eggs (in dozens) depends on the price (in dollars) of the eggs. During one week, the rancher sold 2,500 one-dozen cartons of eggs at $0.77 per dozen. During another week, the rancher sold 3,000 one-dozen cartons of eggs at $0.72 per dozen. In a third week, the rancher sold 3,500 one-dozen cartons of eggs at $0.69 per dozen.
a. Find a linear model by hand. Be sure to show all work.
b. Use a graphing calculator to find the linear regression equation for this data.
c. Are your two equations the same? Why or why not?
3. Complete the Excursion on pp. 385 – 386.
4. Match each of the following functions with the graph that best describes the situation.
a. The cost of building a house as a function of its square footage.
b. The height of an egg dropped from a 300-foot building as a function of time.
c. The height of a human as a function of time.
d. The demand for Big Macs as a function of price.
e. The height of a child on a swing as a function of time.
5. Karen, who is standing on the ground, is throwing an apple to her brother, Jim, who is standing on the balcony of their home. The height , in feet, of the apple above the ground seconds after it is thrown is given by . If Jim’s outstretched arms are 18 feet above the ground, will the apple ever be high enough so that he can catch it?
6. The number of bass in a lake is given by , where is the number of months that have passed since the lake was stocked with bass.
a. How many bass were in the lake immediately after it was stocked?
b. How many bass were in the lake 1 year after the lake was stocked?
c. What will happen to the bass population as increases without bound?
d. What does your answer in part c mean?
7. Consider the following scenario: Barbara decides to take a walk. She leaves home, walks 2 blocks in 5 minutes at a constant speed, and realizes that she forgot to lock the door. So, Barbara runs home in 1 minute. While at her doorstep, it take her 1 minute to find her keeys and lock the door. Barbara walks 5 blocks in 15 minutes and then decides to jog home. It take her 7 minutes to get home. Draw a graph of Barbara’s distance from home (in blocks) as a function of time.
8. The function models the typing speed , in words per minute, of a student months after the student completes a typing class.
a. What is the student’s typing speed, to the nearest word per minute, 1 month, 3 months, and 10 months, after the student completes the class?
b. Consider your answers to part a. What does this mean?
9. A Boeing 747 crosses the Atlantic Ocean (3,000 miles) with an airspeed of 500 miles per hour. The cost (in dollars) per passenger is given by , where is the ground speed (airspeed wind).
a. What is the cost per passenger for quiescent (no wind) conditions?
b. What is the cost per passenger with a head wind of 50 miles per hour?
c. What is the cost per passenger with a tail wind of 100 miles per hour?
Self-Reflection
Write a short (one or two paragraphs) self-reflection of this homework assignment. What were your strengths? What were some areas in which you could improve?